7. A proton is travelling In a circle Perpendicularly to a magnetic field of 0.3

Question

7. A proton is travelling In a circle Perpendicularly to a magnetic field of 0.3T. If the radius of the orbit is 1.7 m, what is the speed of the proton? 8. Suppose you nave a circular coil that has 120,000 loops of wire wrapped around a cylinder with radius 0.3 m. The axis of the coil is perpendicular to the earth's magnetic field (B= 0.4 Gauss). You then rotate the loop at 150 Hz. What is the peak current that will flow in a 2000 Ohm resistor connected across ends of the coil? 9. Look at the AC circuit below, Find the total impedance of the circuit and find the phase difference between the current through the AC source and its voltage.

Explanation / Answer

7)

Charge of proton

Q=1.6*10-19C

mass of proton

m=1.67*10-27 kg

Centripetal force =magnetic force

mv2/r=qvB

=>v=qBr/m =(1.6*10-19)*0.3*1.7/(1.67*10-27)

v=5.1*107 m/s

8)

Area of circular coil

A=pi*r2=pi*0.32=0.2827 m2

angular frequency

W=2pi*f=2pi*150=942.48 rad/s

1 gauss =0.0001 tesla

B=0.4*0.0001=4*10-5 T

Maximum Induced emf

Emax=NBAW =120,000*4*10-5*0.2827*942.48

Emax=1279.1 Volts

Peak Current

Ipeak=Emax/R =1279.1/2000

Ipeak=0.6396 A =0.64 A(approx)

9)

Inductive reactance

XL=2pi*f*L=2pi*5000*(5*10-3)=157.08 ohms

Impedance

Z=sqrt[R2+XL2]=sqrt[902+157.082]

Z=181.03 ohms

b)

phase difference

o=tan-1(XL/R)=tan-1(157.08/90)

o=60.190=60.2o

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